Never use of after despite.
✗ Recycling is a good way to manage waste despite of its cost.
✓ Recycling is a good way to manage waste despite its cost.
✗ Many people are successful in their jobs despite of the fact that they have no university diploma.
✓ Many people are successful in their jobs despite the fact that they have no university diploma.
You can also use the phrase in spite of in the same way:
Recycling is a good way to manage waste in spite of its cost.
Despite and in spite of mean exactly the same, but despite is much more frequent.